A satellite based positioning of a device is supported by various Global Navigation Satellite Systems (GNSS). These include for example the American Global Positioning System (GPS), the Russian Global Orbiting Navigation Satellite System (GLONASS), the future European system GALILEO, the Space Based Augmentation System (SBAS), the Japanese GPS augmentation Quasi-Zenith Satellite System (QZSS), the Locals Area Augmentation System (LAAS), and hybrid systems.
It is the general idea of GNSS positioning to receive satellite signals at a receiver, which is to be positioned, and to determine the time it took the signals to propagate from a respective satellite to the receiver. This time of flight can be determined for example based on a measured time of arrival of the satellite signal at the receiver and based on information on the time of transmission of the signal at the satellite, which is included in the received signal. By multiplying the time of flight with the speed of light, it is converted to the distance between the receiver and the respective satellite. Further, the positions of the satellites at the respective time of transmission are estimated, for example based on information included in the signal.
The computed distances and the estimated positions of the satellites then permit a calculation of the current position of the receiver, since the receiver is located at an intersection of the distances from a set of satellites.
The assumption that the distance between the receiver and a respective satellite can be obtained by multiplying the determined time of flight of a satellite signal with the speed of light is based on a simplification, though. A signal traveling from a satellite to a GNSS receiver passes through the electrically neutral atmosphere, including the troposphere and the stratosphere. This electrically neutral atmosphere comprises different and varying refractive indices at different locations. The variability of the refractive index causes the satellite signals to be affected by a path delay and by ray bending. The effect is commonly known as tropospheric delay or slant delay. It is difficult to compensate fully for the tropospheric delay. It constitutes one of the major residual error sources in GNSS navigation solutions.
For correcting the delay, it is generally assumed that the atmosphere is horizontally layered and azimuthally symmetric. The tropospheric delay may then be determined as a sum of two components, namely a hydrostatic component and a non-hydrostatic component. The hydrostatic component is due to atmospheric gases that are in hydrostatic equilibrium, including usually dry gases and part of the water vapor. The non-hydrostatic component is due water vapor in the atmosphere that is not in hydrostatic equilibrium. Moreover, each of these components can be expressed as the product of the delay experienced by the GNSS signals in the zenith direction and a mapping function, which models the elevation angle dependency of the tropospheric delay. With such an approach, the total tropospheric delay Z(ε) of a particular satellite signal can be determined according to the following equation:Z(ε)=Zh·mh(ε)+Zw·mw(ε)  (1)
Here, Zh is the hydrostatic zenith delay, that is, the delay due to a hydrostatic influence that would be experienced by a signal traveling from a satellite to the receiver, when the satellite is located at the zenith of the receiver. Further, mh(ε) is the hydrostatic mapping function for a given elevation angle ε of a satellite at the current position of the receiver. Zw is the non-hydrostatic zenith delay, that is, the delay due to a non-hydrostatic influence that would be experienced by a signal traveling from a satellite to the receiver, when the satellite is located at the zenith of the receiver. Further, mw(ε) is the non-hydrostatic mapping function for a given elevation angle ε of a satellite at the current position of the receiver. A satellite at the zenith of a receiver has an elevation angle of 90°.
There are various known approaches for determining the zenith delay, like the Hopfield model or the SAAS model for the hydrostatic zenith delay and the Mendes model, the SAAS model, the Ifadis model or the Hopfield model for the non-hydrostatic zenith delay. Further, the zenith delay could be determined using numerical weather model data.
Typical troposphere delay models moreover use mapping functions in the form of continued fractions. The hydrostatic mapping function mh and the wet mapping function mw for an elevation angle ε may take for example the following form:
                                          m                          h              /              w                                ⁡                      (            ɛ            )                          =                              1            +                                          a                0                                            1                +                                                      a                    1                                                        1                    +                                          a                      2                                                                                                                              sin              ⁡                              (                ɛ                )                                      +                                          a                0                                                              sin                  ⁡                                      (                    ɛ                    )                                                  +                                                      a                    1                                                                              sin                      ⁡                                              (                        ɛ                        )                                                              +                                          a                      2                                                                                                                              (        2        )            
For most existing mapping functions, the values of parameters a0, a1 and a2 in equation (2) are determined separately for the hydrostatic delay and for the non-hydrostatic delay based on values of meteorological parameters, such as surface pressure and temperature. Examples are the Herring mapping functions, the Niell Mapping Functions (NMF), the Isobaric Mapping Functions (IMF) and the Vienna Mapping Functions (VMF). The Global Mapping Function (GMF) is moreover an empirical mapping function that is based on numerical weather model data. The model is determined by using a 15×15 degrees grid of monthly mean profiles for pressure, temperature and humidity from the European Centre for Medium-Range Weather Forecasts (ECMWF).
While equations (1) and (2) are based on the assumption that the atmosphere is azimuthally symmetric, pressure, temperature and humidity gradients may cause in addition in horizontal gradients in the refractivity field. This azimuthal asymmetry may introduce significant errors in measurements where high precision is required. To take account of this effect, it is possible to distinguish between the azimuthally symmetric delay, also referred to as isotropic delay, and asymmetric parts of the delay, also referred to as anisotropic delay. While above equation (1) for the total tropospheric delay only includes the isotropic delay, it can be supplemented by a third term for the anisotropic delay as follows:Z(ε,φ)=Zh·mh(ε)+Zw·mw(ε)+mg(ε)cot ε(z0 cos φ+z1 sin φ)  (3)
In this equation, z0 and z1 are path delay gradient parameters, for instance vertically integrated refractivity gradients, in the North and East direction, respectively. The parameter φ is the azimuth angle at which a satellite is visible at a GNSS receiver, and mg is a special mapping function for the gradient term. It has to be noted that the anisotropic part of the equation could also be determined separately for hydrostatic and non-hydrostatic delay. A combination does not cause a significant loss of accuracy, though. Further, it has to be noted that the mapping function mg is not critical and can be chosen equal to mh or mw.
In many situations, in particular with mobile GNSS receivers, meteorological parameter values are not available and nominal global parameter sets that are based on long term statistics are used for correcting tropospheric delays. Such global troposphere models, however, are not accurate enough for high precision positioning applications.
In some geodetic surveying applications, which are used for bridge constructions etc., zenith delay corrections and surface meteorological parameters are sent to the user, for example in the RINEX (receiver independent exchange) format. RINEX atmospheric corrections are mostly used in post processing, though, not in real time. The transmitted values are moreover limited to a particular position and have no ability to adjust, if the location or the altitude of the user changes. Further, the time dependency of the provided values is not taken into account, as it is assumed that a new parameter set is transmitted at short intervals, for example every second.
If a GNSS receiver is integrated into a wireless terminal or if a GNSS receiver is an accessory for a wireless terminal, the GNSS receiver may be assisted in the positioning by a wireless communication network. The wireless communication network may provide assistance data, which is received by the wireless terminal and used for improving the performance of the GNSS receiver. In addition, the wireless terminal may provide measurement results of the GNSS receiver to the wireless communication network, which performs the required positioning computations.
The availability of assistance data can greatly affect the performance of a GNSS receiver. The format in which assistance data may be sent to a wireless terminal is specified in various wireless communication standards. Control Plane solutions include Radio Resource Location Services Protocol (RRLP) in Global System for Mobile Communications (GSM), Rate Range Correction (RRC) in Wideband Code Division Multiple Access (W-CDMA) and IS-801.1/IS-801.A in Code Division Multiple Access (CDMA). Broadcast assistance data information elements for GSM are defined in 3GPP Technical Specification 44.035, V6.0.0: “Broadcast network assistance for Enhanced Observed Time Difference (E-OTD) and Global Positioning System (GPS) positioning methods”. Finally, there are User Plane solutions OMA SUPL 1.0 by the Open Mobile Alliance, and various proprietary solutions for CDMA networks.
The assistance data that is provided according to current wireless standards may include for example a reference time, a reference location, clock correction data and ephemeris data, which describes a section of a satellite path for a short period of time, etc. However, it does not support a GNSS signal propagation delay estimation.